My area of research is algebraic geometry and commutative algebra (MSC 14 and 13).

My dissertation was titled "Multiplier Ideals of Line Arrangements". I computed the multiplier ideals of general arrangements of lines through the origin in C^3, and even for "most" special arrangements. I studied under Rob Lazarsfeld at University of Michigan.

I am interested in a range of problems involving algebraic geometry and commutative algebra, usually with a combinatorial or computational flavor. Roughly, my interests group under: arrangements (of hyperplanes, points, etc); multiplier ideals (computation, applications to commutative algebra); secant varieties, computing rank, and Hilbert functions; and computer experimentation in mathematics.

List of publications

  1. Bounding symbolic powers via asymptotic multiplier ideals, Ann. Acad. Pedagog. Crac. Stud. Math. 8 (2009), 67--77; Link to journal, Link to arXiv
  2. (with Christopher Hillar, Luis Garcia-Puente, Abraham Martin del Campo, James Ruffo, Stephen L. Johnson, Frank Sottile) Experimentation at the Frontiers of Reality in Schubert Calculus; submitted; Link to arXiv
  3. (with Nero Budur and Mircea Mustata) The Monodromy Conjecture for hyperplane arrangements; submitted; Link to arXiv
  4. (with J.M. Landsberg) On the ranks and border ranks of symmetric tensors; to appear in Found. Comput. Math.; Link to journal, Link to arXiv
  5. (with Ulrich Derenthal, Michael Joyce) The nef cone volume of generalized Del Pezzo surfaces, Algebra & Number Theory 2 (2008), no. 2, 157--182; Link to journal, Link to arXiv
  6. A note on Mustata's computation of multiplier ideals of hyperplane arrangements, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1575--1579; Link to journal, Link to arXiv
  7. On the intersection of the curves through a set of points in P^2, J. Pure Appl. Algebra 209 (2007), no. 2, 571--581; Link to journal, Link to arXiv
  8. Multiplier ideals of general line arrangements in C^3, Comm. Alg. 35 (2007), no. 6, 1902--1913; Link to journal, Link to arXiv

In preparation

  1. (with Susan Cooper and Brian Harbourne) Bounding Hilbert functions of fat points in the plane via matroids and residuation
  2. (with Javier Elizondo, Paulo Lima-Filho, and Frank Sottile) Arithmetic toric varieties

Expository writing

  1. Some time ago, I began work on a short expository set of notes on Chern classes in algebraic geometry, particularly in the context of enumerative problems. The notes are not polished. Some day I hope to finish them; in the meantime, I have uploaded a draft, in PDF format (21 pages): An informal introduction to computing with Chern classes (Oct. 31, 2004).
  2. Some expository notes based on talks I gave in the TAMU Several Complex Variables seminar in February 2008 on multiplier ideals, aimed at relating resolution of singularities to the problem of simplifying integrals. (July 16, 2008: v0.2. Numerous minor improvements.)

Multiplier ideals

Occasionally people ask me for suggestions of expository introductions to multiplier ideals. I have made a list.

Here is a modest collection of links to pages which in turn link to interesting sources for algebraic geometry.

zteitler@tamu.edu   Back to front page.